`A=[[1, tan x],[-tan x,1]]`, show that `A^(T)A^(-1)=[[cos 2x,-sin 2x],[sin 2x,cos 2x]]`.

A=[{:(1 ,tanx),(-tanx," "1):}] "show that"" "A^(T)A^(-1)=[{:(cos2x,-sin2x),(sin2x,cos2x):}].

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is

Show that sin^-1 x+cos^-1 x=pi/2 .

tan^-1[(cos x)/(1+sin x)] is equal to

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x )

(sin^(2) x)/(1 + cos x)

show that 2^(sin x)+2^(cos x)ge2^(1-(1)/sqrt(2))

Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x .

Prove that sin^(6)x + cos^(6)x = 1 - 3 sin^(2) x cos^(2)x .

Solve sin x-3 sin 2x+sin 3x=cos x-3 cos 2x+cos 3x